Pqrs is a parallelogram. given that three of the vertices are p(6,-2,4), q(2,4,-8), and r(-2,2,4), determine the coordinates of vertex s.

the vertex and vertices are the same thing but i do not know how to find the fourth point using the distance formula. can someone me?

  S = (2, -4, 16)

Step-by-step explanation:

You don't need the distance formula to find the fourth vertex. The midpoint of the diagonals is the same for both diagonals, so ...

  (P+R)/2 = (Q+S)/2 . . . . midpoints are the same

  P + R = Q + S . . . . . . . .multiply by 2

  P + R - Q = S . . . . . . . .subtract Q to get an equation for S

S = (6, -2, 4) +(-2, 2, 4) -(2, 4, -8)

  = (6 -2 -2, -2 +2 -4, 4 +4 +8)

S = (2, -4, 16)

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